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POWER problem on physics? |
Cycling. For a touring bicyclist the drag coefficient is 1, the frontal area is 0.463 m^2, and the coefficient of rolling friction is 0.0045. The rider has a mass of 50 kg, and her bike has mass 12 kg. a.) To maintain a speed of 12 m/s (about 27 mi/h) on a level road, what must the rider's power output to the rear wheel be? b.) For racing, the same rider uses a different bike with a coefficient of rolling friction 0.0030 and mass 9 kg. She also crouches down, reducing her drag coefficient to 0.88 and reducing her frontal area to 0.366 m^2. What must her power output to the rear wheel be then to maintain a speed of 12 m/s. c.) For the situation in part (b), what power output is required to maintain a speed of 6 m/s? Note the great drop in power requirement when the speed is only halved. Assume no wind, grav. accel. = 9.80665, and air density=1.2 kg/m^3, and friction is ideal, that is, independent of speed when speed>0. Note that if you ignore friction the power required due to aero drag is proportional to v^3. The formulas are: fa = .5 *a * cd * rho * v^2 (fa=aero force, a=area, cd=drag coeff, rho=density, v=velocity) ff = m * g * cf (ff=friction force, m=mass, g=grav accel, cd=friction coeff) power=v * (fa + ff) Answers (forces in N, power in W):: fa-----------ff----------Power a. 40.0032 2.736055 512.8711 b. 27.82771 1.735777 354.7619 c. 6.956928 1.735777 52.15623 |
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